Solve (x-3)^2-7=0

$$( x - 3 ) ^ { 2 } - 7 = 0$$

Solve for x

$$x=\sqrt{7}+3\approx 5.645751311$$

$$x=3-\sqrt{7}\approx 0.354248689$$

Steps by Finding Square Root

Add 7 to both sides of the equation.

$$\left(x-3\right)^{2}-7+7=7$$

Subtracting 7 from itself leaves 0.

$$\left(x-3\right)^{2}=7$$

Take the square root of both sides of the equation.

$$x-3=\sqrt{7} x-3=-\sqrt{7}$$

Add 3 to both sides of the equation.

$$x-3-\left(-3\right)=\sqrt{7}-\left(-3\right) x-3-\left(-3\right)=-\sqrt{7}-\left(-3\right)$$

Subtracting -3 from itself leaves 0.

$$x=\sqrt{7}-\left(-3\right) x=-\sqrt{7}-\left(-3\right)$$

Subtract -3 from \sqrt{7}.

$$x=\sqrt{7}+3$$

Subtract -3 from -\sqrt{7}.

$$x=3-\sqrt{7}$$

The equation is now solved.

$$x=\sqrt{7}+3 x=3-\sqrt{7}$$